BC 3
Sequences and Series Quiz
Name:
No Calculators allowed.
Show set-up/method clearly on all problems unless instructed otherwise.
#1.
Complete (no work necessary):
a. The sequence an  r n converges to
if and only if
<r<

b. The series
r
k
converges to
if and only if
<r<
k 1

e. An expression of the form
a
k 1
k
is called an
.
Corresponding to this, we have the sequence {Sn}, which is called the
. The nth term of this sequence is given by Sn =
The sequence {an} is called
.
If lim(an )  0 then
.
n 
#2(5 pts) Find an expression for the sequence of partial sums, S n , for the series

1
1 
  k  k  2  . Use this to determine whether the series converges or diverges. If the
k 1
series converges, find the value.
.
#3(9 pts) Determine whether each series is geometric. If it is, either determine its sum or
state that it diverges. For those geometric series containing an x, state clearly the limits on
the variable x for which the series converges.
2k
 k 
3
2 4 8
a. 1   

3 9 27
b.
2 3 4
1  

3 9 27

k

3k
c. ( x  3)  ( x  3)3  ( x  3)5  ( x  3)7 
 ( x  3) 2 k 1 
#4(5 pts) Find an explicit formula for the sequence:
1
1
1
1
1,  4 2 ,  9  4 , 16  6 ,  258 , ........................ .
Determine whether this sequence converges. If so, find the limit showing all steps
clearly. If not, explain.